Fundamentals of Electromagneticsfor Teaching and

LearningA Two-Week Intensive Course for Faculty

inElectrical-, Electronics-, Communication-, and

Computer- Related Engineering Departments in

Engineering Colleges in India

- by
- Nannapaneni Narayana Rao
- Edward C. Jordan Professor Emeritus
- of Electrical and Computer Engineering
- University of Illinois at Urbana-Champaign, USA
- Distinguished Amrita Professor of Engineering
- Amrita Vishwa Vidyapeetham, India

Program for Hyderabad Area and Andhra Pradesh

FacultySponsored by IEEE Hyderabad Section, IETE

Hyderabad Center, and Vasavi College of

EngineeringIETE Conference Hall, Osmania

University CampusHyderabad, Andhra PradeshJune

3 June 11, 2009 Workshop for Master Trainer

Faculty Sponsored byIUCEE (Indo-US Coalition for

Engineering Education)Infosys Campus, Mysore,

KarnatakaJune 22 July 3, 2009

Introductory PresentationPart 2

Terminology

- Because I will be using the term electrical and

computer engineering it is of interest to

elaborate upon this terminology. In engineering

departments in the United States educational

institutions, electrical and computer engineering

is generally one academic department, although

not in all institutions. The name, ECEDHA,

Electrical and Computer Engineering Department

Heads Association, reflects this situation. In

the College of Engineering at the University of

Illinois at Urbana-Champaign (UIUC), the

Department of Electrical and Computer Engineering

(ECE) offers two undergraduate programs leading

to the Bachelor of Science degrees Electrical

Engineering and Computer Engineering.

The Scope of Electrical Engineering

- A list of the twenty greatest engineering

achievements of the twentieth century compiled by

the National Academy of Engineering includes ten

achievements primarily related to the field of

electrical engineering electrification,

electronics, radio and television, computers,

telephone, internet, imaging, household

appliances, health technologies, and laser and

fiber optics. The remaining achievements in the

list - automobile, airplane, water supply and

distribution, agricultural mechanization, air

conditioning and refrigeration, highways,

spacecraft, petroleum/petrochemical technologies,

nuclear technologies, and high-performance

materials - also require knowledge of electrical

engineering to differing degrees. In the

twenty-first century the discipline of electrical

engineering continues to be one of the primary

drivers of change and progress in technology and

standards of living around the globe.

NAEs List of Greatest Engineering Achievements

of the 20th Century

- Electrification
- Automobile
- Airplane
- Water Supply Distribution
- Electronics
- Radio Television
- Agricultural Mechanization
- Computers
- Telephone
- Air Conditioning Refrigeration

- Highways
- Spacecraft
- Internet
- Imaging
- Household Appliances
- Health Technologies
- Petroleum/Petrochemical Technologies
- Laser Fiber Optics
- Nuclear Technologies
- High-Performance Materials

Red indicates areas where ECE at UIUC has had

influence.

The Scope of Computer Engineering

- Computer engineering is a discipline that

applies principles of physics and mathematics to

the design, implementation, and analysis of

computer and communication systems. The

discipline is broad, spanning topics as diverse

as radio communications, coding and encryption,

computer architecture, testing and analysis of

computer and communication systems, vision, and

robotics. A defining characteristic of the

discipline is its grounding in physical aspects

of computer and communication systems. Computer

engineering concerns itself with development of

devices that exploit physical phenomena to store

and process information, with the design of

hardware that incorporates such devices, and with

software that takes advantage of this hardware's

characteristics. It addresses problems in design,

testing, and evaluation of system properties,

such as reliability, and security. It is an

exciting area to work in, one that has immediate

impact on the technology that shapes society

today.

The Illinois Curriculum in Electrical Engineering

- For the electrical engineering program at

Illinois, the core curriculum focuses on

fundamental electrical engineering knowledge

circuits, systems, electromagnetics, solid state

electronics, computer engineering, and design. A

rich set of elective courses permits students to

select from collections of courses in seven areas

of electrical and computer engineering

bioengineering, acoustics, and magnetic resonance

engineering circuits and signal processing

communication and control computer engineering

electromagnetics, optics, and remote sensing

microelectronics and quantum electronics power

and energy systems.

The Illinois Curriculum in Computer Engineering

- For the computer engineering program, the core

curriculum focuses on fundamental computer

engineering knowledge circuits, systems,

electromagnetics, computer engineering, solid

state electronics, and computer science. A rich

set of elective courses permits students to

concentrate in any sub-discipline of computer

engineering including computer systems

electronic circuits networks engineering

applications software, languages, and theory

and algorithms and mathematical tools.

Electromagnetics is all around us!

- In simple terms, every time we turn a switch on

for electrical power or for an electronic

equipment, every time we press a key on our

computer key board or on our cell phone, or every

time we perform a similar action involving an

everyday electrical device, electromagnetics

comes into play.

Some modern applications of EM (Courtesy of Weng

C. Chew)

Fundamental to the Study of ECE

- It is the foundation for the technologies of

electrical and computer engineering, spanning the

entire electromagnetic spectrum, from dc to

light. As such, in the context of engineering

education, it is fundamental to the study of

electrical and computer engineering.

Foundation for the technologies of electrical and

computer engineering

Fundamental to the Study of ECE

In 1963, the American Institute of Electrical

Engineers (AIEE) and the Institute of Radio

Engineers (IRE) were merged into the Institute of

Electrical and Electronics Engineers (IEEE), a

global nonprofit organization with over 375,000

members, and the world's leading professional

association for the advancement of technology.

The IEEE logo or badge is a merger of the badges

of the two parent organizations. It contains a

vertical arrow surrounded by a circular arrow,

within a kite-shaped border. No letters clutter

the badge because a badge without letters can be

read in any language. The AIEE badge had the kite

shape which was meant to symbolize the kite from

Benjamin Franklins famous kite experiment to

study electricity. The IRE badge had the two

arrows that symbolize the right hand rule of

electromagnetism.

Fundamental to the Study of ECE

Alternatively, the vertical arrow can be thought

of as representing one of the two fields,

electric or magnetic, and the circular arrow

surrounding it representing the second field,

produced by it, so that together they represent

an electromagnetic field.

Fundamental to the Study of ECE

Whether this logo of IEEE was intended to be a

recognition of the fact that electromagnetics is

fundamental to all of electrical and computer

engineering, it is a fact that all electrical

phenomena are governed by the laws of

electromagnetics, and hence, the study of

electromagnetics is essential to all branches of

electrical and computer engineering, and

indirectly impacts many other branches.

EM is so fundamental that even Mac Circuits Van

Valkenburg was caught having fun communicating

the RH Rule to Robert Communications Lucky!

Wonderful picture!

An amusing incident

- One of the earliest postwar programs to be

established at UIUC was a program in radio

direction finding (RDF). It was intended as a

basic research program, sponsored by the Office

of Naval Research. When the sponsor was asked by

the research supervisor, Edward Jordan, what

facets of the field might be of particular

interest, the answer received was Look, you

know Maxwells equations, the Russians know

Maxwells equations you take it from there.

Jordan was amused that it would be difficult to

get more basic than that.

Wullenweber Array at Bondville Road Field Station

of the RDF Laboratory

- Used in Radio Direction Finding Laboratory
- In operation 1955-1980
- Used 120 antennas and was 1000 ft in diameter
- Operated in frequency range of 4-16 MHz

Wullenweber array of the RDF Laboratory (1955

1980)

Discovering Wullenweber while riding the

Pineapple Express at the Dole Plantation on the

island of Oahu, Hawaii, with family on June 4,

2005, as a reminder

Wullenweber and Bananas (My favorite slide)

So, what is Electromagnetics?

By the very nature of the word, electromagnetics

implies having to do with a phenomenon involving

both electric and magnetic fields and furthermore

coupled. This is indeed the case when the

situation is dynamic, that is, time-varying,

because time-varying electric and magnetic fields

are interdependent, with one field producing the

other.

What is Electromagnetics?

In other words, a time-varying electric field or

a time-varying magnetic field cannot exist alone

the two fields coexist in time and space, with

the space-variation of one field governed by the

time-variation of the second field. This is the

essence of Faradays law and Amperes circuital

law, the first two of the four Maxwells

equations resulting in wave propagation.

About Electromagnetics (Continued)

Only when the fields are not changing with time,

that is, for the static case, they are

independent a static electric field or a static

magnetic field can exist alone, with the

exception of one case in which there is a one-way

coupling, electric field resulting in magnetic

field, but not the other way.

About Electromagnetics (Continued)

Thus, in the entire frequency spectrum, except

for dc, all electrical phenomena are, in the

strictest sense, governed by interdependent

electric and magnetic fields, or electromagnetic

fields.

Quasistatic Approximation

However, at low frequencies, an approximation,

known as the quasistatic approximation, can be

made in which the time-varying fields in a

physical structure are approximated to have the

same spatial variations as the static fields in

the structure obtained by setting the source

frequency equal to zero.

Quasistatic Approximation (Continued)

Thus, although the actual situation in the

structure is one of electromagnetic wave nature,

it is approximated by a dynamic but not wavelike

nature. As the frequency becomes higher and

higher, this approximation violates the actual

situation more and more, and it becomes

increasingly necessary to consider the wave

solution.

Statics f 0 dc Dynamics

No restriction complete Maxwells equations

Electromagnetic waves Quasistatics

Low-frequency extension of statics, or

low-frequency approximation of

dynamics

Maxwells Equations are elegant and beautiful.

As profound as they are, they are actually quite

simple to explain and understand.

Maxwells Equations

d

E

d

l

B

d

S

ò

ò

dt

S

C

Charge density

Electric field intensity

Magnetic flux density

d

B

d

S

0

ò

ò

ò

ò

H

d

l

J

d

S

D

d

S

dt

S

S

C

S

Current density

Magnetic field intensity

Displacement flux density

Faradays Law, the first EMantra

Electromotive Force (emf) or voltage around C

Negative of the time rate of increase of

the magnetic flux crossing S bounded by C.

Voltage around C, also known as electromotive

force (emf) around C (but not really a force),

Magnetic flux crossing S,

Time rate of decrease of magnetic flux crossing

S,

Amperes Circuital Law, the second EMantra

Magnetomotive force (mmf) around C Current due

to flow of charges crossing S bounded by C

Time rate of increase of electric (or

displacement) flux crossing S

Magnetomotive force (only by analogy with

electromotive force),

Current due to flow of charges crossing S,

Displacement flux, or electric flux, crossing S,

Time rate of increase of displacement flux

crossing S, or, displacement current crossing S,

- Gauss Law for the Electric Field, the third

EMantra - Displacement flux emanating from a closed

surface S - charge contained in the volume V bounded by S
- charge enclosed by S

r

Gauss Law for the Magnetic Field, the fourth

EMantra

- Magnetic flux emanating from a closed

surface S 0.

Out of the four EMantras, only the first two,

Faradays and Amperes circuital laws are

independent. The fourth Mantra, Gauss law for

the magnetic field, follows from Faradays law,

and the third Mantra, Gauss law for the electric

field, follows from Amperes circuital law, with

the aid of an auxiliary equation, the law of

conservation of charge.

Law of Conservation of Charge, an auxiliary

EMantra

r(t)

- Current due to flow of charges emanating from a

closed surface S - Time rate of decrease of charge enclosed by S.

Maxwells Equations in Differential Form and the

Continuity Equation

Faradays Law

Amperes Circuital Law

Gauss Law for the Electric Field

Gauss Law for the Magnetic Field

Continuity Equation

Time derivatives of the components of B

Lateral space derivatives of the components of E

Charge density

The Mahatmyam (Greatness) of Maxwells Equations

The Mahatmyam (Greatness) of Maxwells Equations

Amperes Circuital Law

Law of Conservation of Charge

Faradays Law

?

Gauss Law for E

The Mahatmyam (Greatness) of Maxwells Equations

Thus, Faraday's law says that a time-varying

magnetic field gives rise to an electric field,

the space-variation of which is related to the

time-variation of the magnetic field. Ampere's

circuital law tells us that a time-varying

electric field produces a magnetic field, the

space variation of which is related to the

time-variation of the electric field. Thus, if

one time-varying field is generated, it produces

the second one, which in turn gives rise to the

first one, and so on, which is the phenomenon of

electromagnetic wave propagation, characterized

by time delay of propagation of signals. In

addition, Amperes circuital law tells us that an

electric current produces a magnetic field, so

that a time-varying current source results in a

time-varying magnetic field, beginning the

process of one field generating the second.

Hertzian Dipole

Radiation from Hertzian Dipole

Hertzian dipole and radiation pattern on the

covers of the U.S. and Indian Editions of

Fundamentals of Electromagnetics

The Contribution of Maxwell

You will have noted that none of the four

equations are named after Maxwell. So, the

question arises as to why they are known as

Maxwells equations. It is because of a purely

mathematical contribution of Maxwell. This

mathematical contribution is the second term on

the right side of Amperes circuital law. Prior

to that, Amperes circuital law consisted of only

the first term on the right side.

The Contribution of Maxwell

Without the second term on the right side of

Amperes circuital law, the loop is not complete

and hence there is no interdependence of

time-varying electric and magnetic fields and no

EM waves!

Unifying Electricity and Magnetism

Thus, the purely mathematical contribution of

Maxwell in 1864 unified electricity and magnetism

and predicted the generation of EM waves owing to

the interdependence of time-varying electric and

magnetic fields. Only 23 years later in 1887,

eight years after his death in 1879, the theory

was proved correct by the experimental discovery

of EM waves by Heinrich Hertz.

- Parallel with Principles from Upanishads
- In fact, Maxwells Equations are as fundamental

to the science of all electrical phenomena and

hence to modern living as the Guiding Principles,

- from the Taittriyopanishad are to spirituality.

The Guiding Principles from Upanishads

The Guiding Equations of Electromagnetics

Maxwells Equations parallel to the Principles in

Upanishads! Isnt it fascinating!

So, why are these poor little guys so perplexed

at the sight of Maxwells Equations?

Why is the teaching and learning of EM so

dreaded, as implied by this mnemonic?

HOW I WANT A DRINK, 3. 1 4 1 5

ALCOHOLIC, OF COURSE, 9 2

6 AFTER THE HEAVY LECTURES 5

3 5 8 INVOLVING ELECTRO-MAGNETICS!

9 7 9

Incomplete list of reasons given

- Abstract (not practical ideal theoretical hard

to understand difficult abstruse) - Mathematical complexity
- Vector notation
- Curl, divergence, and gradient
- Highly conceptual

The approach to the teaching of electromagnetics

While these might be valid reasons to differing

degrees for different people, depending on their

background preparations, let us look at the

teaching of EM.

The approach to the teaching of electromagnetics

Historically, the development of major

technologies based on Maxwells equations

occurred in the sequence of electrically and

magnetically based technologies (electromechanics

and electrical power) in the nineteenth century

electronics hardware and software in the

twentieth century and photonics technologies,

entering into the twenty-first century.

Progression of technologies based on Maxwells

Equations

The approach to the teaching of electromagnetics

The teaching of electromagnetics evolved

following this sequence, that is, beginning with

a course on electrostatics, magnetostatics,

energy and forces, and in some cases quasistatic

fields, followed by Maxwells equations for

time-varying fields and an introduction to

electromagnetic waves. This course was then

followed by one or more courses on transmission

lines, electromagnetic waves, waveguides and

antennas.

The historical, or, inductive approach

The teaching of the introductory course in this

manner is known as the inductive approach, that

is, an approach consisting of developing general

principles from particular facts, which in this

case was developing complete set of Maxwells

equations from the particular laws of static

fields. Since generally much time is taken up

for the coverage of static fields before getting

to the complete set of Maxwells equations, the

time is cut short (and in some cases not

available) for the more interesting and useful

material, centered on electromagnetic waves. This

is the principal drawback of the traditional,

inductive, approach, which is unnecessarily

aggravating, because all the mathematics and

concepts taught in the context of static fields

can not only be taught but taught better and with

less aggravation with time-varying fields.

The Deductive Approach

In contrast to the inductive approach is the

deductive approach, that is, an approach in

which one begins with the general principles that

are accepted as true and then applies it to

particular cases, which in this case is beginning

with the complete set of Maxwells equations for

time-varying fields and then developing their

applications, as well as considering special

cases of static and quasistatic fields. This

approach permits the structuring of the course so

that (a) it constitutes the foundation for

students taking follow-on courses, as well as (b)

imparting the essentials for students taking this

course only in EM.

Deduction versus Induction

Deduction applies to the process in which one

starts with a general principle that is accepted

as true and applies it to a particular case,

arrives at a conclusion that is true if the

starting principle was true, as in All animals

die this is an animal therefore this will die.

Induction applies to the process by which one

collects many particular cases, finds out by

experiment what is common to all of them, and

forms a general rule or principle which is

probably true, as in Every animal I have tested

died probably all animals die.

The Deductive Approach (Continued)

Since the deductive approach begins with the

complete Maxwells equations, it provides an

appreciation of the fact that regardless of how

low the frequency is, as long as it is nonzero,

the phenomenon is one of electromagnetic waves,

resulting from the interdependence of

time-varying electric and magnetic fields. Then,

statics and quasistatics are treated as special

cases.

The Deductive Approach (Continued)

Furthermore, combining the deductive approach

with the thread of statics-quasistatics-waves

makes it quite clear that, along the frequency

spectrum, the quasistatic behavior approached

from the static (zero frequency) limit as an

extension of the static behavior to dynamic

behavior of first order in frequency is the same

as the low-frequency behavior approached from the

other (higher frequencies) side, by approximating

the exact dynamic solution for low frequencies.

This very important concept is not always clearly

understood or appreciated when the inductive

approach is employed.

The approach to the teaching of electromagnetics

And the deductive approach is the way of teaching

Maxwells equations as God said, as contrasted

with the inductive approach, which is the way in

which they were evolved by human intellect. I am

not a philosopher but it should not be difficult

to accept that Maxwell and others did not create

the equations they only discovered what God

said in the first place, through a series of

ingenious steps over time!

Knowledge is inherent man no knowledge comes

from outside. We say Newton discovered

gravitation. Was it sitting anywhere in a corner

waiting for him? It was in his own mind the

time came and he found it out. All knowledge that

the world has ever received comes from the mind

the infinite library of the universe is in your

own mind. The external world is simply the

suggestion, the occasion, which sets you to study

your own mind Swami Vivekananda

So, why is the teaching and learning of EM so

dreaded?

It is not entirely because of EM, but also

because of the way it is taught!

PoEM on why study EM!

To the students from all around the world And to

the students all over the world EMpowered by the

Jordan name And inspired by the AMRITA name I

offer to you this book on EM Beginning with this

poem which I call PoEM If you are wondering why

you should study EM Let me tell you about it by

means of this PoEM First you should know that the

beauty of EM Lies in the nature of its compact

formalism Through a set of four wonderful

EMantras Familiarly known as Maxwell's

equations They might be like mere four lines of

mathematics to you But in them lie a wealth of

phenomena that surround you Based on them are

numerous devices That provide you everyday

services Without the principles of Maxwell's

equations Surely we would all have been in the

dark ages Because there would be no such thing as

electrical power Nor would there be electronic

communication or computer Which are typical of

the important applications of ECE And so you see,

EM is fundamental to the study of ECE.

PoEM on why study EM! (Continued)

So, you are curious about learning EM Let us

proceed further with this PoEM First you should

know that E means electric field And furthermore

that B stands for magnetic field Now, the static

E and B fields may be independent But the dynamic

E and B fields are interdependent Causing them to

be simultaneous And to coexist in any given

space Which makes EM very illuminating And modern

day life most interesting For it is the

interdependence of E and B fields That is

responsible for electromagnetic waves In your

beginning courses you might have learnt circuit

theory It is all an approximation of

electromagnetic field theory So you see they put

the cart before the horse But it is okay to do

that and still make sense Because at low

frequencies circuit approximations are fine But

at high frequencies electromagnetic effects are

prime So, whether you are an electrical

engineer Or you happen to be a computer

engineer Whether you are interested in high

frequency electronics Or may be high-speed

computer communication networks You see,

electromagnetic effects are prime Studying the

fundamentals of EM is sublime.

PoEM on why study EM! (Continued)

If you still have a ProblEM with EM, Because it

is full of abstract mathematics, I say, my dear

ECE student who dislikes electromagnetics Because

you complain it is full of abstract mathematics I

want you to know that it is the power of

mathematics That enabled Maxwells prediction

through his equations Of the physical phenomenon

of electromagnetic radiation Even before its

finding by Hertz through experimentation In fact

it was this accomplishment That partly resulted

in the entitlement For the equations to be known

after Maxwell Whereas in reality they are not his

laws after all For example the first one among

the four of them Is Faradays Law expressed in

mathematical form You see, mathematics is a

compact means For representing the underlying

physics Therefore do not despair when you see

mathematical derivations Throughout your textbook

on the Fundamentals of Electromagnetics Instead

look through the derivations to understand the

concepts Realizing that mathematics is only a

means to extend the physics Think of you as

riding the horse of mathematics To conquer the

new frontier of electromagnetics Let you and me

together go on the ride As I take you through the

steps in stride, with grattitude!

The End